Sam Baron in The Singularity Hub:
Bees in hives produce hexagonal honeycomb. Why? According to the “honeycomb conjecture” in mathematics, hexagons are the most efficient shape for tiling the plane. If you want to fully cover a surface using tiles of a uniform shape and size while keeping the total length of the perimeter to a minimum, hexagons are the shape to use. Charles Darwin reasoned that bees have evolved to use this shape because it produces the largest cells to store honey for the smallest input of energy to produce wax. The honeycomb conjecture was first proposed in ancient times, but was only proved in 1999 by mathematician Thomas Hales.
Here’s another example. There are two subspecies of North American periodical cicadas that live most of their lives in the ground. Then, every 13 or 17 years (depending on the subspecies), the cicadas emerge in great swarms for a period of around two weeks. Why is it 13 and 17 years? Why not 12 and 14? Or 16 and 18? One explanation appeals to the fact that 13 and 17 are prime numbers. Imagine the cicadas have a range of predators that also spend most of their lives in the ground. The cicadas need to come out of the ground when their predators are lying dormant.
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